On the von Mises-Sternberg version of Saint-Venant's principle in plane linear elastostatics
type: Item
instance of: scholarly article
title: On the von Mises-Sternberg version of Saint-Venant's principle in plane linear elastostatics
zbMATH Open document ID: 0829.73019
DOI: 10.1007/BF00386245
author: P. Maremonti
author: Remigio Russo
published in: Archive for Rational Mechanics and Analysis
publication date: 1996-01-17T00:00:00Z
review text: The von Mises-Sternberg version of Saint-Venant's principle for a homogeneous isotropic elastic body subject to continuous surface traction fields (cf. The linear theory of elasticity, by \textit{M. E. Gurtin} [Encyclopedia of Physics Vol. VIa/2, pp. 190-196 (1972; Zbl 0277.73001)]) is extended to include a nonhomogeneous anisotropic but plane elastic body. The elasticity tensor \(\mathbb{C}\) is assumed to be bounded and measurable, so weak solutions to the governing equations are dealt with. Due to nonregularity of the first derivatives of the solutions, the strains are estimated in Morrey norms if \(\mathbb{C}\) is at most continuous, and in Hölder norms if \(\mathbb{C}\) is Hölder continuous. The estimation technique is based on a number of a priori estimates and some lemmas from functional analysis. The reviewer believes that the results obtained hold only if the problem is formulated in a dimensionless form. Otherwise, one can not calculate, for example, a norm in \(C^{0, \alpha}\) (except for \(\alpha= 0\)) in the main theorem, or use Hardy's inequality (6.2), etc. No mention is made, however, what system of units has been chosen to make the problem dimensionless.
reviewed by: Józef Ignaczak
Mathematics Subject Classification ID: 74G50
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 754035
zbMATH Keywords: nonhomogeneous anisotropic body
zbMATH Keywords: surface traction
zbMATH Keywords: elasticity tensor
zbMATH Keywords: weak solutions
zbMATH Keywords: Morrey norms
zbMATH Keywords: Hölder norms
zbMATH Keywords: functional analysis
MaRDI profile type: Publication
cites work: Q3900391
cites work: Q5537959
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full work available at URL: https://doi.org/10.1007/bf00386245
OpenAlex ID: W1999479843
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description: scientific article; zbMATH DE number 754035